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CHARACTERIZATION OF ELLIPSOIDS BY MEANS OF PARALLEL TRANSLATED SECTIONS
Author(s) -
Larman D.,
Montejano L.,
Morales-Amaya E.
Publication year - 2010
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579310000379
Subject(s) - ellipsoid , mathematics , section (typography) , convex body , regular polygon , characterization (materials science) , combinatorics , geometry , convex hull , computer science , geodesy , geography , physics , optics , operating system
Let K be a convex body and let p 0 ∈int K . Suppose that in every direction we can choose continuously a section of K which is a translated copy of the corresponding parallel section of K through p 0 . Our main result essentially claims that if all these pairs of sections are different almost everywhere, then K is an ellipsoid.